1. SWITCHING CONTROL DESIGN
Daniel Liberzon
Coordinated Science Laboratory and
Dept. of Electrical & Computer Eng.,
Univ. of Illinois at Urbana-Champaign

2. HYBRID FEEDBACK Plant: P Classical continuous feedback paradigm: C P
But logical decisions
are often necessary:
The closed-loop
system is hybrid u y C1 C2
l o g i c P

3. REASONS for SWITCHING Nature of the control problem
Sensor or actuator limitations
Large modeling uncertainty
Discuss all three briefly
The first one: Brockett’s necessary condition
One way out - hybrid feedback
Combinations of the above

4. REASONS for SWITCHING Nature of the control problem
Sensor or actuator limitations
Large modeling uncertainty
Combinations of the above
Discuss all three briefly
The first one: Brockett’s necessary condition
One way out - hybrid feedback

5. PARKING PROBLEM Nonholonomic constraint: wheels do not slip
Explain the equations
Explain the constraint
This is controllable nonholonomic: can move anywhere eventually, but there are constraints on where can move
instantaneously
Parking problem is not solvable with continuous feedback
Nonholonomic constraint: wheels do not slip

6. OBSTRUCTION to STABILIZATION?
Draw arrows to explain the singularity
Can move away from the line for an arbitrary time
This is not just discontinuous feedback: there are
two different modes of operation. Discrete state variable
Put back the “Reasons” slide
Solution: move away first